A supplement is something that needs to be added to make something complete - in some respect.
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A supplement to an angle in Geometry is a second angle with a size equal to the difference between 180 degrees and the size of the first angle. If the size of two angles is 180 degrees, then the angles are 'supplementary".
The supplement of an angle is the angle that, when added to the original angle, equals 180 degrees. Therefore, to find the supplement of 135 degrees, we subtract 135 from 180. The supplement of 135 degrees is 45 degrees.
A complementary angle adds to 90 degrees or pi/2 radians. A supplementary angle adds to 180 degrees or pi radians.
Well, honey, the supplement of a 10 degree angle is 170 degrees. So if you add those two angles together, you'll get a nice, straight line of 180 degrees. Simple math, darling.
The question asks for the complement of (the supplement of (80 degrees) ). We have to find the supplement of 80 first, and then find the complement of the supplement. The supplement of an angle is (180 - the angle). The complement of an angle is (90 - the angle). The supplement of 80 degrees is (180 - 80) = 100 degrees. The complement of that supplement is (90 - 100) = -10 degrees.